FOM: Mathematics and Physics -- some details

[Vaughan R. Pratt]

>From: Solomon Feferman <sf at Csli.Stanford.EDU>
>6. On these and related matters, I have consulted my distinguished
>colleagues in applied mathematics, Joe Keller and George Papanicolao.
>A communication from the latter concluded with: "I cannot think of a
>compelling physical situation where non-measurability or
>non-separability are essential."  

How could it be otherwise?  Given that our experimental data concerning
the universe is finite and likely to remain so, it would appear
intrinsically impossible to demonstrate the need in physics for any
infinity, let alone the higher infinities.

>From: jshipman at bloomberg.net
>I showed ("Cardinal conditions for strong Fubini theorems", T.A.M.S.
>10/90) that the existence of their nonmeasurable functions was
>independent of ZFC.  They'd used CH to get non-Fubini functions
>(Martin's axiom would also work); I showed it was consistent with ZFC
>(and implied by RVM) that there were none.

Although the storehouses of experimental evidence on magnetic tapes and
hard drives in laboratories around the world are finite, they are
vast.  The approximation of "a lot" by "infinity" is a mathematical
technique, and the question of whether *such approximations*
necessarily lead to higher infinities is a question not about physical
situations but about mathematical techniques.

Papanicolao talks of physical situations while Shipman talks of
properties of the mathematics some people use in physics.  Where is the
conflict?

Vaughan Pratt